Codebook generating method and apparatus for generating a codebook for multi-polarized multiple-input multiple-output (MIMO) systems

ABSTRACT

A terminal and method for generating a codebook for a multiple-input multiple-output (MIMO) system is provided. The codebook generation includes: assigning a single-polarized precoding matrix to diagonal blocks among a plurality of blocks arranged in a block diagonal format in which a number of diagonal blocks corresponds to a number of polarization directions of transmitting antennas; and assigning a zero matrix to remaining blocks excluding the diagonal blocks.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/242,490, filed on Sep. 23, 2011, which is a continuation of U.S.patent application Ser. No. 12/025,910, filed on Feb. 5, 2008, nowissued as U.S. Pat. No. 8,050,357, and which claims the benefit of U.S.Provision Application No. 60/899,634, filed on Feb. 6, 2007 and U.S.Provision Application No. 60/929,032, filed on Jun. 8, 2007 in the U.S.Patent and Trademark office, and Korean Patent Application No.2007-28878, filed on Mar. 23, 2007 and Korean Patent Application No.2007-95490, filed on Sep. 19, 2007 in the Korean Intellectual PropertyOffice, the disclosures of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

Aspects of the present invention relate to a multiple-inputmultiple-output (MIMO) system, and more particularly, to a codebook ofprecoding matrices for use in MIMO systems and a method of generating acodebook for use in such MIMO systems.

2. Description of the Related Art

Currently, wireless communication technologies for providing a varietyof multimedia services in wireless communication environments areexpanding. High-speed data transmission is needed to provide highquality multimedia services in wireless communication systems.Accordingly, various research has been conducted to support high-speeddata transmission in such wireless communication systems. A recentproposal to achieve high-speed data transmission relates to the use ofmultiple antennas at both the transmitter and the receiver, known asmultiple-input multiple-output (MIMO) systems.

MIMO technology offers significant increases in channel capacities withlimited frequency resources and in data transmission rates by usingmultiple antennas at both the transmitter and the receiver. In such MIMOsystems, a number of antennas are used when scattering conditions aresubstantial, and theoretically, MIMO systems provide channel capacitiesproportional to the number of antennas. Such MIMO technology can serveas an important component of the next generation mobile communicationsystems, such as 3^(rd) Generation Partnership Project (3GPP), Super 3G(or 3G Long Term Evolution “LTE”), 3GPP2 and upcoming 4G systems,particularly, for the downlink from a single base station to multipleuser equipments.

However, when MIMO technology is deployed, the physical space and areafor installing antennas may be limited. Communication systems using MIMOtechnology are highly affected by spacing between antennas.Specifically, as the spacing between antennas becomes smaller, highercorrelation between wireless channels can be generated. Particularly,when antennas have the same polarization, higher correlation betweenwireless channels can be generated. Correlation generated betweenwireless channels reduces reliability for data communication and alsoreduces data transmission rates.

Accordingly, various methods of using the polarization direction ofantennas are needed in order to reduce an area for installing multipleantennas and also to increase channel capacities. When multi-polarizedantennas are used in MIMO systems, Correlation between wireless channelscan be reduced.

Coding operations, referred to as a precoding, are needed to effectivelytransmit data, via wireless channels, in MIMO systems to maximize systemperformance and capacity. Precoding represents multi-layer beamformingin which a transmission signal (data) is emitted from each of theantennas in accordance with a data precoding rule, i.e., appropriatephase (and gain) weighting such that the signal power is maximized atthe receiver input and the multipath fading effect is minimized. Theweight can be expressed in terms of a precoding matrix (i.e., a set ofbeam-forming vectors) and is selected from a set of precoding matricesin a codebook.

Currently, there are various types of codebooks designed for theparticular cases of single-polarized MIMO schemes where the polarizationof antennas is single-polarization. However, no effective codebook hasbeen offered in association with cases of multi-polarized MIMO schemeswhere the polarization of antennas is multi-polarization. Existingcodebooks designed for single-polarized MIMO schemes cannot be optimizedfor multi-polarized MIMO schemes.

Accordingly, there is a need for a method and apparatus for generating acodebook for a MIMO system with low complexity and excellentperformance, even when the polarization of antennas ismulti-polarization.

SUMMARY OF THE INVENTION

Aspects of the present invention provide a method and apparatus forgenerating a codebook for a multi-polarized multiple-inputmultiple-output (MIMO) system that can generate a precoding matrix usinga single-polarized precoding matrix even when the polarization ofantennas is multi-polarization, and thereby obtain an excellentprecoding matrix that is easily generated.

Additional aspects and/or advantages of the invention will be set forthin part in the description which follows and, in part, will be obviousfrom the description, or may be learned by practice of the invention.

Aspects of the present invention also provide a method and apparatus forgenerating a codebook in a multi-polarized MIMO system that canreconstruct a precoding matrix according to a transmission rank.

Aspects of the present invention also provide a method and apparatus forgenerating a codebook in a multi-polarized MIMO system that can generatea rotated matrix when the polarization direction of transmittingantennas is rotated, which can flexibly cope with a change in thepolarization direction.

According to an aspect of the present invention, there is provided amethod of generating a codebook for use in a multi-polarized MIMO, themethod including: assigning a single-polarized precoding matrix to eachof diagonal blocks among a plurality of blocks arranged in a blockdiagonal structure in which a number of diagonal blocks corresponds to anumber of polarization directions of transmitting antennas; andassigning a zero matrix to each of remaining blocks excluding thediagonal blocks within the block diagonal structure.

According to another aspect of the present invention, the codebookgeneration method may further include: generating a precoding matrix formulti-polarized MIMO by combining the single-polarized precodingmatrices assigned to the diagonal blocks and the zero matrices assignedto the remaining blocks within the block diagonal structure.

According to another aspect of the present invention, the codebookgeneration method may further include: reconstructing the precodingmatrix by selecting, from the precoding matrix, at least one columnvector according to a transmission rank corresponding to a number ofdata streams to be transmitted.

According to another aspect of the present invention, the codebookgeneration method may further include: generating a rotated precodingmatrix using the precoding matrix and a rotated matrix corresponding toa rotated angle of the polarization direction when the polarizationdirection of transmitting antennas is rotated.

According to another aspect of the present invention, the codebookgeneration method may further include: adjusting a phase of each ofelements included in the reordered matrix using a diagonal matrix.

According to another aspect of the present invention, there is providedan apparatus for generating a codebook for multi-polarized MIMO, theapparatus including: a single-polarized precoding matrix assignment unitto assign a single-polarized precoding matrix to each of diagonal blocksamong a plurality of blocks arranged in a block diagonal structure inwhich a number of diagonal blocks corresponds to a number ofpolarization directions of transmitting antennas; and a zero matrixassignment unit to assign a zero matrix to each of remaining blocksexcluding the diagonal blocks within the block diagonal structure.

In addition to the example embodiments and aspects as described above,further aspects and embodiments will be apparent by reference to thedrawings and by study of the following descriptions.

BRIEF DESCRIPTION OF THE DRAWINGS

A better understanding of the present invention will become apparentfrom the following detailed description of example embodiments and theclaims when read in connection with the accompanying drawings, allforming a part of the disclosure of this invention. While the followingwritten and illustrated disclosure focuses on disclosing exampleembodiments of the invention, it should be clearly understood that thesame is by way of illustration and example only and that the inventionis not limited thereto. The spirit and scope of the present inventionare limited only by the terms of the appended claims. The followingrepresents brief descriptions of the drawings, wherein:

FIGS. 1A-1C illustrate multi-polarized transmitting/receiving antennasin a MIMO system according to example embodiments of the presentinvention;

FIG. 2 is a flowchart illustrating a method of generating a codebook ofprecoding matrices for use in a multi-polarized MIMO system according toan example embodiment of the present invention;

FIG. 3 illustrates a precoding matrix for use in a multi-polarized MIMOsystem according to an example embodiment of the present invention;

FIG. 4 illustrates precoding matrices where a discrete Fourier transform(DFT) precoding matrix is assigned to diagonal blocks in amulti-polarized MIMO system according to an example embodiment of thepresent invention; and

FIG. 5 is a block diagram illustrating a codebook generation apparatusfor generating a codebook of precoding matrices for use in amulti-polarized MIMO system according to an example embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE EXAMPLE EMBODIMENTS

Reference will now be made in detail to present embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings, wherein like reference numerals refer to the like elementsthroughout. The embodiments are described below in order to explain thepresent invention by referring to the figures.

Prior to describing embodiments of the present invention in detail,examples of current codebooks designed for single-polarized MIMOincluding a discrete Fourier transform (DFT) codebook and a rotated DFTcodebook are provided herein below to help understanding theconstruction of the new codebook for the particular case ofmulti-polarized MIMO. For example, a DFT codebook providing a DFTprecoding matrix for use in a single-polarized MIMO system may berepresented as follows:γ={U ⁽⁰⁾ ,U ⁽¹⁾ , . . . ,U ⁽² ^(B) ⁻¹}:Precoding matrix setU ^((b)) =[u ₀ ^((b)) . . . u _(M-1) ^((b)) ]:bth precoding matrixu _(m-1) ^((b)) :mth column vector in the matrix U ^((b)),  [Equation 1]

where B is the number of bits necessary to indicate one of those 2^((B))DFT precoding matrices, M is a number of transmitting antennas, γ is aDFT codebook that is a set of DFT precoding matrices, and U^((b)) is theb^(th) DFT precoding matrix. The m^(th) column vector in the matrixU^((b)) may be represented as u_(m-1) ^((b)). Specifically, the DFTcodebook includes 2^((B)) DFT precoding matrices. Each of the 2^((B))DFT precoding matrices includes M column vectors.

Also, each of the DFT precoding matrices is an M×M matrix, and u_(m-1)^((b)) is a vector having m elements and may be a column vector having asize of M×1.

In the DFT codebook, u_(m) ^((b)) may be defined as follows:

$\begin{matrix}{{u_{m}^{(b)} = {\frac{1}{\sqrt{M}}\begin{bmatrix}u_{0m}^{(b)} & \ldots & u_{{({M\mspace{14mu} 1})}m}^{(b)}\end{bmatrix}}^{T}}u_{nm}^{(b)} = {\exp{\left\{ {j\frac{2\pi\; n}{M}\left( {m + \frac{b}{2^{B}}} \right)} \right\}.}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

That is, 2^((B)) DFT precoding matrices exist in the DFT codebook. EachDFT precoding matrix is an M×M matrix. Also, each of the M×M DFTprecoding matrices includes M column vectors. Each column vector may bean M×1 column vector, and elements of the column vector may bedetermined as in the above Equation 2.

For example, when the polarization of two (2) transmitting antennas aresingle-polarization, the DFT precoding matrix may include two matricesgiven as follows,

$\begin{matrix}{\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix},\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

In contrast to the current DFT codebook for single-polarized MIMOsystem, a rotated DFT codebook is a set of rotated DFT precodingmatrices for use in a single-polarized MIMO system. Such a rotated DFTcodebook may be represented as follows:

$\begin{matrix}{{\begin{Bmatrix}{E,} & {E^{2},} & \ldots & E^{2^{B}}\end{Bmatrix}\text{:}\mspace{14mu}{such}\mspace{14mu}{that}\mspace{14mu} U^{(i)}}\overset{\Delta}{=}{E^{i + 1}.}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

An i^(tb) rotated DFT precoding matrix may be represented as follows:

$\begin{matrix}{{E^{(i)} = {\begin{bmatrix}e^{j\;\theta_{0}} & 0 & \ldots & 0 \\0 & e^{j\;\theta_{1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & e^{j\;\theta_{M - 1}}\end{bmatrix}{DFT}_{M}}},} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

where DFT_(M) is a DFT precoding matrix in the single-polarized MIMOsystem. The rotated DFT precoding matrix DFT_(M) is generated byrotating all the elements, included in each of rows of the DFT precodingmatrix, by a particular phase.

Also, in a MIMO system, a transmitting antenna located at a transmitterside transmits a data signal, via a wireless channel, to a receivingantenna located at a receiver side. The wireless channel may be referredto as a channel matrix H. In a multi-polarized MIMO system, the channelmatrix H may be modeled as H=X⊙H′. Here, the symbol “⊙” denotes aHadamard product of matrices and has a calculation rule, as given by:

$\begin{matrix}{{\begin{bmatrix}a & b \\c & d\end{bmatrix}\mspace{11mu}{\begin{bmatrix}x & y \\z & w\end{bmatrix}}} = {\begin{bmatrix}{ax} & {by} \\{cz} & {dw}\end{bmatrix}.}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

Hereinafter, the present invention will be described in detail withreference to the accompanying drawings.

Turning now to FIGS. 1A-1C, various combinations of dual-polarizedtransmitting/receiving antennas for multi-polarized MIMO channelsaccording to example embodiments of the present invention areillustrated.

Referring to FIG. 1A, a MIMO system 110 includes two transmittingantennas (2Tx) 111 and 112 arranged at a transmitter side, and tworeceiving antennas (2Rx) 113 and 114 arranged at a receiver side. Thetwo transmitting antennas 111 and 112 are perpendicular to each other.Accordingly, the polarization directions of signals transmitted, via awireless channel (i.e., channel matrix H), by the transmitting antennas111 and 112 are orthogonal to each other.

For 2Tx-2Rx: Precoding matrix X may be represented as follows:

$X = \begin{bmatrix}1 & \sqrt{\chi} \\\sqrt{\chi} & 1\end{bmatrix}$

The parameter χ, called depolarization factor, can be thought of as aglobal XPD (cross polarization discrimination) of the antennas and thechannel. The exact value of the depolarization factor can be difficultto quantify as it depends upon many factors and will vary from onewireless environment to another. Such a depolarization factor can coverthe wide range of values of values 0≦χ≦1.

Similarly, another MIMO system 120, as shown in FIG. 1B, includes fourtransmitting antennas (4Tx) 121, 122, 123, and 124 arranged at atransmitter side, and two receiving antennas (2Rx) 125 and 126 arrangedat a receiver side. The polarized directions of signals transmitted, viaa wireless channel (i.e., channel matrix H), by two transmittingantennas 121 and 122 and remaining two transmitting antennas 123 and 124are orthogonal to each other.

For 4Tx-2Rx: Precoding matrix X may be represented as follows:

$X = \begin{bmatrix}1 & 1 & \sqrt{\chi} & \sqrt{\chi} \\\sqrt{\chi} & \sqrt{\chi} & 1 & 1\end{bmatrix}$

Also, still another MIMO system 130, as shown in FIG. 1C, includes fourtransmitting antennas (4Tx) 131, 132, 133, and 134 arranged at atransmitter side, and four receiving antennas (4Rx) 135, 136, 137, and138 arranged at a receiver side.

For 4Tx-4Rx: Precoding matrix X may be represented as follows:

$\begin{matrix}{{X = \begin{bmatrix}1 & 1 & \sqrt{\chi} & \sqrt{\chi} \\1 & 1 & \sqrt{\chi} & \sqrt{\chi} \\\sqrt{\chi} & \sqrt{\chi} & 1 & 1 \\\sqrt{\chi} & \sqrt{\chi} & 1 & 1\end{bmatrix}},} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

where χ is a real number, and 0≦χ≦1.

Referring to Equation 7, the first column and the second column of thematrix X correspond to two transmitting antennas (2Tx) 121 and 122, andthe third column and the fourth column of the matrix X correspond toother two transmitting antennas (2Tx) 123 and 124.

Specifically, the channel matrix H may be modeled as: H=X⊙H′. Also, whenfour transmitting antennas (4Tx) and four receiving antennas (4Rx) arearranged in the MIMO system 130, shown in FIG. 1C, the precoding matrixX may be a 4×4 matrix, as shown in Equation 7. Also, the fourtransmitting antennas (4Tx) 131, 132, 133, and 134 transmit signals intwo polarization directions. As a result, the matrix X may be modeled asa precoding matrix having the two blocks in a diagonal direction.

When a distance between transmitting antennas (Tx) and receivingantennas (Rx) is small, that is, for example, when the user equipment(UE) is close to the base station (BS), parameter χ, calleddepolarization factor, may be modeled close to zero “0”. Conversely,when a distance between transmitting antennas (Tx) and receivingantennas (Rx) is great, that is, for example, when there are large cellswithin the wireless networks, χ may be modeled close to one “1”.Accordingly, when χ changes from “0” to “1”, that is, within the rangeof 0≦χ≦1, the codebook should have excellent performance in both asingle-polarized MIMO system and a multi-polarized MIMO system.

FIG. 2 is a flowchart illustrating a method of generating a codebook foruse in a multi-polarized MIMO system according to an example embodimentof the present invention. Such a codebook is provided with a set ofunitary matrices designed not only for multi-polarized MIMO schemes, butalso single-polarized MIMO schemes without any significant performancedegradation. The codebook for such multi-polarized MIMO can beconstructed in a block diagonal structure, known as a block diagonalmulti-polarized codebook. Similarly, a precoding matrix for use in amulti-polarized MIMO in such a block diagonal structure can be expressedin terms of M×N, where M indicates a number of transmitting antennas ata transmitter side and N indicates a number of data streams in thematrix X. The size of such a matrix may be determined according to atransmission rank (spatial multiplexing rate) corresponding to at leastone of the number of transmitting antennas and the number of datastreams to be transmitted, via the wireless channels. For example, ifthe number of transmitting antennas (Tx) is four (4) and thetransmission rank, that is, the number of data streams is also four (4),then the size of the matrix may be 4×4.

Such a matrix (block diagonal multi-polarized codebook) may be organizedor modeled as having a plurality of blocks according to a number ofpolarization directions of transmitting antennas within a block diagonalstructure. Blocks in a diagonal direction are known as diagonal blocks.In an M×N matrix, the term “diagonal direction” refers to a directionfrom an element of a first column and a first row to an element in anM^(th) column and N^(th) row. For example, when a 4×4 matrix is dividedinto four sets of 2×2 matrices, a 2×2 matrix that includes elements,included in either the first (1st) or second (2^(nd)) column and alsoincluded in either the first (1st) or second (2^(nd)) row of the matrix,and another 2×2 matrix that includes elements, included in either thethird (3rd) or fourth (4^(th)) column and also included in either thethird (3rd) or fourth (4^(th)) row of the matrix, are characterized as“diagonal blocks.”

In this instance, when the number of polarization directions oftransmitting antennas is two (2), the total number of diagonal blocksmay be two (2) and the total number of remaining blocks within the blockdiagonal structure may be two (2). Similarly, when the number ofpolarization directions of transmitting antennas is three (3), the totalnumber of diagonal blocks may be three (3) and the total number ofremaining blocks may be six (6).

Referring to FIG. 2, in operation S210, a single-polarized precodingmatrix is assigned to each of diagonal blocks among a plurality ofblocks within the diagonal block structure. Such a single-polarizedprecoding matrix is a precoding matrix designed for single-polarizedMIMO.

For example, the single-polarized precoding matrix assigned to thediagonal blocks in such a block diagonal multi-polarized codebook mayinclude a DFT precoding matrix or a rotated DFT precoding matrixselected in a matrix codebook designed for single-polarized MIMO, e.g.,the DFT codebook or the rotated DFT codebook or any other matrixcodebook. Any one of the DFT precoding matrix and the rotated DFTprecoding matrix may be assigned to diagonal blocks.

In addition, the size of the single-polarized precoding matrix may bedetermined according to the number of transmitting antennas (Tx) havingthe same polarization direction. For example, it is assumed that thetotal number of transmitting antennas (Tx) is eight (8), and thepolarization direction by two transmitting antennas (2Tx) is a directionx and the polarization direction by the remaining six transmittingantennas (6Tx) is a direction y. In this case, the direction x isperpendicular to the direction y. Also, the number of polarizationdirections is two (2), that is, the directions x and y. Accordingly, theprecoding matrix for multi-polarized MIMO may have two diagonal blocks.

Also, the number of rows of the single-polarized precoding matrix thatare assigned to one diagonal block may be six (6) and the number of rowsof the single-polarized precoding matrix that are assigned to theremaining one diagonal block may be two (2). In this case, if thetransmission rank is eight (8), more specifically, if the transmissionrank of two antennas having the direction x as the polarizationdirection is two (2) and the transmission rank of six antennas havingthe direction y as the polarization direction is six (6), a 2×2single-polarized precoding matrix may be assigned to any one of twodiagonal blocks and a 6×6 single-polarized precoding matrix may beassigned to the other one of the two diagonal blocks.

In operation S220, a zero matrix is assigned to each of the remainingblocks, excluding the diagonal blocks, within the block diagonalstructure.

Specifically, the zero matrix of which all the elements are ‘0’ isassigned to blocks that are not the diagonal blocks among the blocksthat are obtained within the block diagonal structure according to thenumber of polarization directions of transmitting antennas.

In operation S230, a precoding matrix for multi-polarized MIMO, i.e., ablock diagonal multi-polarized codebook is then generated by combiningthe single-polarized precoding matrices assigned to the diagonal blocksand the zero matrices assigned to the remaining blocks within the blockdiagonal structure.

For example, if four transmitting antennas (4Tx) exist, and twotransmitting antennas (2Tx) thereof have the direction x as thepolarization direction and the remaining two transmitting antennas (2Tx)have the direction y as the polarization direction, the codebook for themulti-polarized MIMO system may include a 4×4 matrix as provided, forexample, by:

$\begin{matrix}{\begin{bmatrix}1 & 1 & 0 & 0 \\j & {- j} & 0 & 0 \\0 & 0 & 1 & 1 \\0 & 0 & j & {- j}\end{bmatrix},{\begin{bmatrix}1 & 1 & 0 & 0 \\1 & {- 1} & 0 & 0 \\0 & 0 & 1 & 1 \\0 & 0 & 1 & {- 1}\end{bmatrix}\mspace{14mu}\ldots}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

The two multi-polarized precoding matrices of Equation 8 are only anexample of the present invention. Multi-polarized precoding matrices maybe generated by randomly combining the two DFT precoding matrices ofEquation 3, for example, assigned to the diagonal blocks with the twozero matrices assigned to the remaining blocks within the block diagonalstructure.

Specifically, the precoding matrix for the multi-polarized MIMO systemmay be generated by organizing the precoding matrix into the pluralityof blocks according to the number of polarization directions oftransmitting antennas, and assigning the single-polarized precodingmatrix to the diagonal blocks among all blocks. The zero matrix is thenassigned to each of the remaining blocks within the block diagonalstructure.

For example, when it is assumed that four transmitting antennas existand the number of polarization directions of transmitting antennas istwo (2), the size of the precoding matrix for multi-polarized MIMO maybe 4×4. Also, since the number of polarization directions oftransmitting antennas is two (2), the precoding matrix may be organizedinto a total of four (4) blocks according to the number of polarizationdirections. The precoding matrix for multi-polarized MIMO (blockdiagonal multi-polarized codebook) is then generated by assigning thesingle-polarized precoding matrix to each of the two (2) diagonal blocksand assigning the zero matrix to each of the two (2) remaining blocksthat are not the two (2) diagonal blocks within the block diagonalstructure.

In operation S240, the precoding matrix (block diagonal multi-polarizedcodebook) is then reconstructed by selecting, from the same precodingmatrix, at least one column vector according to a transmission rankcorresponding to a number of data streams to be transmitted, via thewireless channel.

For example, it may be assumed that if four transmitting antennas have amulti polarization, a 4×4 precoding matrix is generated. The 4×4precoding matrix is given by:

$\begin{matrix}{\begin{bmatrix}1 & 1 & 0 & 0 \\1 & {- 1} & 0 & 0 \\0 & 0 & 1 & 1 \\0 & 0 & 1 & {- 1}\end{bmatrix}.} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

Referring to Equation 9, when the transmission rank is two (2), theprecoding matrix (block diagonal multi-polarized codebook) may bereconstructed by selecting two column vectors from four column vectorsincluded in the precoding matrix. Specifically, the precoding matrix ofEquation 9 may be reconstructed to generate six precoding matriceshaving a size of 4×2, as given by:

$\begin{matrix}{\begin{bmatrix}1 & 1 \\1 & {- 1} \\0 & 0 \\0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 \\0 & 0 \\1 & 1 \\1 & {- 1}\end{bmatrix},\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & 1\end{bmatrix},\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix},\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & 1\end{bmatrix},{\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}.}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

When the number of transmitting antennas is M and the transmission rankis r, an M×M precoding matrix may be generated. Also, an M×r precodingmatrix may be generated by selecting column vectors according to thetransmission rank and reconstructing the precoding matrix.

Specifically, according to the present invention, unnecessary columnvectors may be removed from the precoding matrix by reconstructing theprecoding matrix according to the transmission rank, and thus a codebookmay be efficiently generated.

In operation S250, when the polarization direction of transmittingantennas is rotated, a rotated precoding matrix is generated using theprecoding matrix and a rotated matrix. The rotated matrix may correspondto a rotated angle of polarization direction of transmitting antennas(Tx).

The array structure of transmitting antennas may be variously embodied.For example, in the multi-polarized MIMO system, transmitting antennascorresponding to one polarization direction may be installed verticallywith respect to a reference plane and transmitting antennascorresponding to another polarization direction may be installedhorizontally with respect to the reference plane. Also, the transmittingantennas corresponding to one polarization direction may be installed ina direction of +45 degrees with respect to the reference plane andtransmitting antennas corresponding to the other polarization directionmay be installed in a direction of −45 degrees with respect to thereference plane.

Specifically, when the polarization direction of transmitting antennasis rotated by a particular angle with respect to the reference plane, adata stream must be beam formed using the rotated precoding matrix. Therotated precoding matrix may be generated by rotating the precodingmatrix. Specifically, the rotated precoding matrix may be generated bymultiplying the precoding matrix and the rotated matrix.

For example, when it is assumed that respective two transmittingantennas among four transmitting antennas are installed in a directionof +45 degrees and in a direction of −45 degrees with respect to thereference plane, the rotated matrix may be represented as follows:

$\begin{matrix}{U_{rot} = {\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}.}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

The rotated matrix U_(rot) may be multiplied by a random complex value.The resulting structure when multiplying the rotated matrix U_(rot) bythe random scalar value falls within the scope of the present invention.

When the precoding matrix is referred to as W^(BD), the rotatedprecoding matrix W_(RBD) that is generated by rotating the precodingmatrix W_(BD) may be represented as follows:

$\begin{matrix}{W_{RBD} = {\frac{1}{2}U_{rot}W_{BD}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Referring to Equation 12, the rotated matrix U_(rot) may be determinedto correspond to the rotated angle of polarization direction oftransmitting antennas.

According to the present invention, even when various types of arraysare provided, such as transmitting antennas with a rotated polarizationdirection, the rotated precoding matrix may be readily generated usingthe rotated matrix.

In operation S250, a reordered matrix is obtained by reordering columnvectors that are included in the precoding matrix, and the reorderedmatrix and the rotated matrix are used to generate a rotated precodingmatrix.

For example, it is assumed that when two respective transmittingantennas among four transmitting antennas are installed in a directionof +45 degrees and in a direction of −45 degrees with respect to thereference plane, the precoding matrix W_(BD) is generated. In thisinstance, the rotated matrix U_(rot) is the same as Equation 11. Theprecoding matrix W_(BD) is represented as follows:

$\begin{matrix}{W_{BD} = {\begin{bmatrix}1 & 1 & 0 & 0 \\{- 1} & 1 & 0 & 0 \\0 & 0 & 1 & 1 \\0 & 0 & {- 1} & 1\end{bmatrix}.}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack\end{matrix}$

When column vectors included in the precoding matrix W_(BD) of Equation13 are reordered, the reordered matrix W_(reorder,BD) may be representedas follows:

$\begin{matrix}{W_{{reorder},{BD}} = {\begin{bmatrix}1 & 0 & 1 & 0 \\{- 1} & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\0 & {- 1} & 0 & 1\end{bmatrix}.}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack\end{matrix}$

By using the reordered matrix reorder, W_(reorder,BD) and the rotatedmatrix U_(rot) of Equation 11, the rotated precoding matrix W_(RBD) maybe generated and a data stream may be beam formed using the rotatedprecoding matrix W_(RBD), represented as follows:

$\begin{matrix}\begin{matrix}{W_{RBD} = {\frac{1}{2}U_{rot}W_{BD}}} \\{= {{\frac{1}{2}\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}}\begin{bmatrix}1 & 0 & 1 & 0 \\{- 1} & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\0 & {- 1} & 0 & 1\end{bmatrix}}} \\{= {\frac{1}{2}\begin{bmatrix}1 & {- 1} & 1 & {- 1} \\{- 1} & 1 & 1 & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & {- 1} & 1 & 1\end{bmatrix}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

Referring to Equation 15, it may be seen that when two respectivetransmitting antennas among four transmitting antennas are installed ina direction of +45 degrees and in a direction of −45 degrees withrespect to the reference plane, the rotated precoding matrix W_(RBD)corresponding to the precoding matrix W_(BD) of Equation 13 may begenerated like Equation 15.

In operation S260, a phase of each of elements included in the reorderedmatrix is adjusted. The phase of each of elements included in thereordered matrix may be adjusted using a diagonal matrix. In thisinstance, the diagonal matrix includes diagonal elements. Also, thephase of each of the diagonal elements may be the same or different fromeach other. The amplitude of each diagonal element is set to ‘1’. Theamplitude of each of remaining elements, excluding the diagonalelements, is set to ‘0’.

The diagonal matrix is associated with a modulation scheme of datasymbols, instead of increasing channel capacities of the MIMO system,and the like. For example, when the data symbol is modulated usingquadrature phase shift keying (QPSK), the diagonal matrix may changeonly the phase of the data symbol, but may not affect channel capacitiesof the MIMO system.

In this instance, it is assumed that the precoding matrix W_(BD) and thereordered matrix W_(reorder,BD) are given by:

$\begin{matrix}{{W_{BD} = \begin{bmatrix}1 & 1 & 0 & 0 \\j & {- j} & 0 & 0 \\0 & 0 & 1 & 1 \\0 & 0 & j & {- j}\end{bmatrix}},{W_{{reorder},{BD}} = {\begin{bmatrix}1 & 0 & 1 & 0 \\j & 0 & {- j} & 0 \\0 & 1 & 0 & 1 \\0 & j & 0 & {- j}\end{bmatrix}.}}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack\end{matrix}$

In this instance, the phase of each element included in the reorderedmatrix W_(reorder,BD) may be adjusted like Equation 17 below, and datasymbols may be beam formed by using W′_(reorder,BD). Equation 17 isgiven by:

$\begin{matrix}\begin{matrix}{W_{{reorder},{BD}}^{\prime} = {W_{{reorder},{BD}}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & j & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & j\end{bmatrix}}} \\{= \begin{bmatrix}1 & 0 & 1 & 0 \\j & 0 & {- j} & 0 \\0 & j & 0 & j \\0 & {- 1} & 0 & 1\end{bmatrix}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack\end{matrix}$

Aspects of the present invention may be recorded in computer-readablemedia including program instructions to implement various operationsembodied by a computer. The media may also include, alone or incombination with the program instructions, data files, data structures,and the like. Examples of computer-readable media include magnetic mediasuch as hard disks, floppy disks, and magnetic tape; optical media suchas CD ROM disks and DVD; magneto-optical media such as optical disks;and hardware devices that are specially configured to store and performprogram instructions, such as read-only memory (ROM), random accessmemory (RAM), flash memory, and the like. Examples of programinstructions include both machine code, such as produced by a compiler,and files containing higher level code that may be executed by thecomputer using an interpreter. The described hardware devices may beconfigured to act as one or more software modules in order to performthe operations of the above-described embodiments of the presentinvention.

FIG. 3 illustrates a precoding matrix for use in a multi-polarized MIMOsystem according to an example embodiment of the present invention.

Referring to FIG. 3, when the number of transmitting antennas is four(4) and the number of polarization directions of transmitting antennasis two (2), U indicates a precoding matrix for the multi-polarized MIMOsystem. Matrices such as an ‘A’ matrix 310 and a ‘B’ matrix 320, asshown in FIG. 3, indicate a single-polarized precoding matrix, that is,a precoding matrix selected from a matrix codebook designed forsingle-polarized MIMO, e.g., DFT codebook or rotated DFT codebook or anyother matrix codebook, and two ‘0’ matrices 330 and 340 indicate zeromatrices.

Since the number of polarization directions of transmitting antennas istwo (2), two diagonal blocks and two remaining blocks exist. The ‘A’matrix 310 and the ‘B’ matrix 320, that is, single-polarized precodingmatrices, are assigned to the diagonal blocks respectively. The ‘0’matrices 330 and 340, that is, zero matrices, are assigned to theremaining blocks respectively.

The size of the ‘A’ matrix 310 and the ‘B’ matrix 320 may be determinedaccording to the number of transmitting antennas having the samepolarization direction.

For example, when the polarization directions of transmitting antennasare a direction x and a direction y, the number of polarizationdirections of transmitting antennas may be two (2). Also, it may beassumed that when a total number of transmitting antennas is four (4),the polarization direction of two transmitting antennas is the directionx and the polarization direction of the remaining two transmittingantennas is the direction y. In this instance, the ‘A’ matrix 310 may bea single-polarized precoding matrix corresponding to the polarizationdirection of the direction x. Since the number of transmitting antennashaving a polarization direction in the direction x is two (2), thenumber of rows of the ‘A’ matrix 310 may be two (2). Also, the number ofrows of the ‘B’ matrix 320 may be two (2).

When the transmission rank for the direction x is two (2), the number ofrows of the ‘A’ matrix 310 may be two (2). Also, when the transmissionrank for the direction y is two (2), the number of rows of the ‘B’matrix 320 may be two (2).

FIG. 4 illustrates single-polarized precoding matrices, such as, DFTprecoding matrices assigned to diagonal blocks in a multi-polarized MIMOsystem according to an example embodiment of the present invention.

Referring to FIG. 4, W_(BD,1) and W_(BD,2) are precoding matrices whenthe number of transmitting antennas is four (4), the number ofpolarization directions of transmitting antennas is two (2), and thenumber of transmitting antennas having the same polarization directionis two (2).

The DFT precoding matrices that are assigned to diagonal blocks of theprecoding matrices W_(BD,1) and W_(BD,2) can be represented as follows:

$\begin{matrix}{\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix},{\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}.}} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack\end{matrix}$

An example of reordered matrices W_(reorder,BD,1), W_(reorder,BD,2),W_(reorder,BD,3), W_(reorder,BD,4), W_(reorder,BD,5), W_(reorder,BD,6),W_(reorder,BD,7) and W_(reorder,BD,8) that are generated by reorderingcolumn vectors included in the precoding matrices W_(BD,1) and W_(BD,2)may be represented as follows:

$\begin{matrix}{{{W_{{reorder},{BD},1} = \begin{bmatrix}1 & 0 & 1 & 0 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & 1 \\0 & 1 & 0 & {- 1}\end{bmatrix}},{W_{{reorder},{BD},2} = \begin{bmatrix}0 & 1 & 0 & 1 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\1 & 0 & {- 1} & 0\end{bmatrix}},{W_{{reorder},{BD},3} = \begin{bmatrix}1 & 0 & 1 & 0 \\j & 0 & {- j} & 0 \\0 & 1 & 0 & 1 \\0 & j & 0 & {- j}\end{bmatrix}},{W_{{reorder},{BD},4} = \begin{bmatrix}0 & 1 & 0 & 1 \\0 & {- j} & 0 & j \\1 & 0 & 1 & 0 \\{- j} & 0 & j & 0\end{bmatrix}},{W_{{reorder},{BD},5} = \begin{bmatrix}0 & 1 & 0 & 1 \\0 & j & 0 & {- j} \\1 & 0 & 1 & 0 \\j & 0 & {- j} & 0\end{bmatrix}},{W_{{reorder},{BD},6} = \begin{bmatrix}1 & 0 & 1 & 0 \\{- 1} & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\0 & {- 1} & 0 & 1\end{bmatrix}}}{{W_{{reorder},{BD},7} = \begin{bmatrix}0 & 1 & 0 & 1 \\0 & {- 1} & 0 & 1 \\1 & 0 & 1 & 0 \\{- 1} & 0 & 1 & 0\end{bmatrix}},{W_{{reorder},{BD},8} = {\begin{bmatrix}1 & 0 & 1 & 0 \\{- j} & 0 & j & 0 \\0 & 1 & 0 & 1 \\0 & {- j} & 0 & j\end{bmatrix}.}}}} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack\end{matrix}$

The reordered matrices may be multiplied by a diagonal matrix. In thisinstance, diagonal elements of the diagonal matrix are complex numbersthat have the size of 1, and remaining elements are 0. The diagonalmatrix does not affect channel capacities or beam forming performance,and is associated with a modulation scheme of data symbols.

For example, the phase of each element included in the reorderedmatrices using random diagonal matrices may be adjusted as shown inEquation 20. In this instance, diagonal elements of a diagonal matrixD_(i) may be random complex numbers that have the magnitude 1.

$\begin{matrix}{{{\begin{matrix}{W_{C,1} = {W_{{reorder},{BD},1}{\quad{\quad D_{1}}}}} \\{= {\begin{bmatrix}1 & 0 & 1 & 0 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & 1 \\0 & 1 & 0 & {- 1}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}1 & 0 & 0 & 0 \\0 & {- 1} & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & {- 1}\end{matrix} \right\rbrack,}}}}\end{matrix}\begin{matrix}{{{W_{C,2} = W_{{reorder},{BD},2}}\quad} D_{2}} \\{= {\begin{bmatrix}0 & 1 & 0 & 1 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\1 & 0 & {- 1} & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{- 1} & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & {- 1}\end{matrix} \right\rbrack,}}}}\end{matrix}}\quad}{\quad{\begin{matrix}{W_{C,3} = {W_{{reorder},{BD},3}D_{3}}} \\{{= {\begin{bmatrix}1 & 0 & 1 & 0 \\j & 0 & {- j} & 0 \\0 & 1 & 0 & 1 \\0 & j & 0 & {- j}\end{bmatrix}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & j & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & j\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{C,4} = {W_{{reorder},{BD},4}D_{4}}} \\{= {\begin{bmatrix}0 & 1 & 0 & 1 \\0 & {- j} & 0 & j \\1 & 0 & 1 & 0 \\{- j} & 0 & j & 0\end{bmatrix}{\quad{\begin{bmatrix}{- 1} & 0 & 0 & 0 \\0 & j & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & {- j}\end{bmatrix},}}}}\end{matrix}\begin{matrix}{W_{C,5} = {W_{{reorder},{BD},5} D_{5}}} \\{= {\begin{bmatrix}0 & 1 & 0 & 1 \\0 & j & 0 & {- j} \\1 & 0 & 1 & 0 \\j & 0 & {- j} & 0\end{bmatrix}{\quad{\begin{bmatrix}{- 1} & 0 & 0 & 0 \\0 & {- j} & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & j\end{bmatrix},}}}}\end{matrix}\begin{matrix}{W_{C,6} = {W_{{reorder},{BD},6}D_{6}}} \\{{= {\begin{bmatrix}1 & 0 & 1 & 0 \\{- 1} & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\0 & {- 1} & 0 & 1\end{bmatrix}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{C,7} = {W_{{reorder},{BD},7}D_{7}}} \\{{= {\begin{bmatrix}0 & 1 & 0 & 1 \\0 & {- 1} & 0 & 1 \\1 & 0 & 1 & 0 \\{- 1} & 0 & 1 & 0\end{bmatrix}\begin{bmatrix}{- 1} & 0 & 0 & 0 \\0 & {- 1} & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{C,8} = {W_{{reorder},{BD},8}D_{8}}} \\{= {\begin{bmatrix}1 & 0 & 1 & 0 \\{- j} & 0 & j & 0 \\0 & 1 & 0 & 1 \\0 & {- j} & 0 & j\end{bmatrix}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & {- j} & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & {- j}\end{bmatrix}}}\end{matrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack\end{matrix}$

Also, a rotated precoding matrix W_(RBD,i) may be generated from W_(C,i)that is generated using the reordered matrix W_(reorder,BD,i) and thediagonal matrix D_(i). More specifically, the rotated precoding matrixW_(RBD,i) may be generated through a mathematical transformation of theprecoding matrices W_(BD,1) and W_(BD,2).

In this instance, when a reordered matrix is generated from theprecoding matrix, and W_(C,i) is generated by multiplying the reorderedmatrix and the diagonal matrix, the rotated precoding matrix W_(RBD,i)may be given by:W _(RBD,i)=½U _(rot) W _(C,i)  [Equation 21]

By using Equation 21, the rotated precoding matrix W_(RBD,i) withrespect to W_(C,i) included in Equation 20 may be represented asfollows:

$\begin{matrix}{\begin{matrix}{W_{{RBD},1} = {\frac{1}{2}U_{rot}W_{C,1}}} \\{{= {{\frac{1}{2}\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}}\begin{bmatrix}1 & 0 & 1 & 0 \\1 & 0 & {- 1} & 0 \\0 & {- 1} & 0 & {- 1} \\0 & {- 1} & 0 & 1\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},2} = {\frac{1}{2}U_{rot}W_{C,2}}} \\{{= {{\frac{1}{2}\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}}\begin{bmatrix}0 & 1 & 0 & {- 1} \\0 & 1 & 0 & 1 \\{- 1} & 0 & 1 & 0 \\{- 1} & 0 & {- 1} & 0\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},3} = {\frac{1}{2}U_{rot}W_{C,3}}} \\{{= {{\frac{1}{2}\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}}\begin{bmatrix}1 & 0 & 1 & 0 \\j & 0 & {- j} & 0 \\0 & j & 0 & j \\0 & {- 1} & 0 & 1\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},4} = {\frac{1}{2}U_{rot}W_{C,4}}} \\{= {{\frac{1}{2}\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}}\begin{bmatrix}0 & j & 0 & {- j} \\0 & 1 & 0 & 1 \\{- 1} & 0 & 1 & 0 \\j & 0 & j & 0\end{bmatrix}}}\end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack\end{matrix}$

Referring to Equation 22, when transmitting antennas corresponding toone polarization direction are installed in a direction of +45 degreeswith respect to the reference plane and transmitting antennascorresponding to another polarization direction are installed in adirection of −45 degrees with respect to the reference plane, four (4)rotated precoding matrices may be generated using the rotated matrix. Inthis instance, although four rotated precoding matrices are expressed inEquation 22, it will be apparent to those of ordinary skills in the artthat various types of rotated precoding matrices may be generated usingthe technical spirits of the present invention.

Also, the rotated precoding matrix W_(RBD,i) may be represented asfollows:

$\begin{matrix}{\begin{matrix}{W_{{RBD},5} = {\frac{1}{2}U_{rot}W_{C,5}}} \\{{= {{\frac{1}{2}\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}}\begin{bmatrix}0 & {- j} & 0 & j \\0 & 1 & 0 & 1 \\{- 1} & 0 & 1 & 0 \\{- j} & 0 & {- j} & 0\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},6} = {\frac{1}{2}U_{rot}W_{C,6}}} \\{{= {{\frac{1}{2}\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}}\begin{bmatrix}1 & 0 & 1 & 0 \\{- 1} & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\0 & {- 1} & 0 & 1\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},7} = {\frac{1}{2}U_{rot}W_{C,7}}} \\{{= {{\frac{1}{2}\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}}\begin{bmatrix}0 & {- 1} & 0 & 1 \\0 & 1 & 0 & 1 \\{- 1} & 0 & 1 & 0 \\1 & 0 & 1 & 0\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},8} = {\frac{1}{2}U_{rot}W_{C,8}}} \\{= {{{\frac{1}{2}\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}}\begin{bmatrix}1 & 0 & 1 & 0 \\{- j} & 0 & j & 0 \\0 & {- j} & 0 & {- j} \\0 & {- 1} & 0 & 1\end{bmatrix}}.}}\end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack\end{matrix}$

When calculating the rotated precoding matrix W_(RBD,i) using Equation22 and Equation 23, it may be represented as follows:

$\begin{matrix}{\begin{matrix}{W_{{RBD},1} = {\frac{1}{2}U_{rot}W_{C,1}}} \\{{= {\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},2} = {\frac{1}{2}U_{rot}W_{C,2}}} \\{{= {\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},3} = {\frac{1}{2}U_{rot}W_{C,3}}} \\{{= {\frac{1}{2}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},4} = {\frac{1}{2}U_{rot}W_{C,4}}} \\{{= {\frac{1}{2}\begin{bmatrix}1 & j & {- 1} & {- j} \\{- j} & 1 & {- j} & 1 \\{- 1} & j & 1 & {- j} \\j & 1 & j & 1\end{bmatrix}}},}\end{matrix}{\begin{matrix}{W_{{RBD},5} = {\frac{1}{2}U_{rot}W_{C,5}}} \\{= {\frac{1}{2}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}}}\end{matrix},\begin{matrix}{W_{{RBD},6} = {\frac{1}{2}U_{rot}W_{C,6}}} \\{{= {\frac{1}{2}\begin{bmatrix}1 & {- 1} & 1 & {- 1} \\{- 1} & 1 & 1 & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & {- 1} & 1 & 1\end{bmatrix}}},}\end{matrix}}\begin{matrix}{W_{{RBD},7} = {\frac{1}{2}U_{rot}W_{C,7}}} \\{{= {\frac{1}{2}\begin{bmatrix}1 & {- 1} & {- 1} & 1 \\{- 1} & 1 & {- 1} & 1 \\{- 1} & {- 1} & 1 & 1 \\1 & 1 & 1 & 1\end{bmatrix}}},}\end{matrix}\begin{matrix}{W_{{RBD},8} = {\frac{1}{2}U_{rot}W_{C,8}}} \\{= {{\frac{1}{2}\begin{bmatrix}1 & j & 1 & j \\{- j} & 1 & j & {- 1} \\1 & {- j} & 1 & {- j} \\{- j} & {- 1} & j & 1\end{bmatrix}}.}}\end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack\end{matrix}$

Accordingly, various types of communication apparatusestransmitting/receiving data according to a space-division multipleaccess (SDMA) scheme can perform communication using at least one of theprecoding matrices disclosed in Equation 24. SDMA denotes a technologythat enables a base station to transmit (or receive) signal (i.e., atleast one data stream) to (or from) multiple users in the same bandwidthand time simultaneously, via multiple antennas in order to maximize adata transmission rate and total capacity. Here, the precoding matricesdisclosed in Equation 24 are based on when a transmission rank is 4, butit is possible to generate precoding matrices corresponding to varioustypes of transmission ranks by selecting column vectors of the precodingmatrices disclosed in Equation 24.

Also, the base station (BS) and terminals may store the codebook ofmatrices of Equation 24 in a computer-readable recording medium, etc.When the base station (BS) transmits a pilot signal, each of theterminals may select any one of the stored matrices in response to thepilot signal. In this instance, each of the terminals may select any onematrix based on the state of a wireless channel formed between each ofthe terminals and the base station, and also may select any one matrixbased on an achievable data transmission rate. Also, each of theterminals may select any one color vector from column vectors includedin the selected matrix.

Also, the terminals may feed back to the base station informationassociated with the selected matrix, or information associated with theselected column vector. The information associated with the selectedmatrix may be index information of the selected matrix and theinformation associated with the selected column vector may be indexinformation of the selected column vector.

In this instance, the base station (BS) may select any one of thematrices disclosed in Equation 24, as a precoding matrix, based on theinformation fed back from the terminals. In particular, the base stationmay select the precoding matrix according to a Per-User Unitary RateControl (PU2RC) scheme. The base station (BS) may perform precoding(beam-forming) on a data stream to be transmitted, via transmittingantennas, using the selected precoding matrix.

Specifically, a terminal according to an aspect of the present inventionmay include a signal receiver to receive a pilot signal transmitted froma base station; a codebook storage unit to store a codebook including atleast one W_(i) where i is a natural number of 1 through 8:

${W_{1} = {\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}}},{W_{2} = {\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}}},{W_{3} = {\frac{1}{2}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}}},{W_{4} = {\frac{1}{2}\begin{bmatrix}1 & j & {- 1} & {- j} \\{- j} & 1 & {- j} & 1 \\{- 1} & j & 1 & {- j} \\j & 1 & j & 1\end{bmatrix}}},{W_{5} = {\frac{1}{2}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}}},{W_{6} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & 1 & {- 1} \\{- 1} & 1 & 1 & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & {- 1} & 1 & 1\end{bmatrix}}},{W_{7} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & {- 1} & 1 \\{- 1} & 1 & {- 1} & 1 \\{- 1} & {- 1} & 1 & 1 \\1 & 1 & 1 & 1\end{bmatrix}}},{{W_{8} = {\frac{1}{2}\begin{bmatrix}1 & j & 1 & j \\{- j} & 1 & j & {- 1} \\1 & {- j} & 1 & {- j} \\{- j} & {- 1} & j & 1\end{bmatrix}}};}$a selector to select a target matrix from the stored at least one W_(i)in response to the pilot signal; and an information feedback unit tofeed back information associated with the target matrix to the basestation.

For instance, the selector may select the target matrix from the storedcodebook including at least one W_(i) based on the state of a wirelesschannel formed between the terminal and the base station. Also, theselector may select the target matrix from the stored codebook includingat least one W_(i) based on an achievable data transmission rate. Inaddition, the selector may select the target matrix from the storedcodebook including at least one W_(i) in response to the pilot signal,and select at least one column vector from column vectors included inthe selected target matrix. In this instance, the information feedbackunit may feed back to the base station information associated with theselected target matrix and information associated with the selected atleast one column vector.

Also, a base station according to an aspect of the present invention mayinclude a codebook storage unit arranged to store a codebook includingat least one W_(i) where i is a natural number of 1 through 8:

${W_{1} = {\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}}},{W_{2} = {\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}}},{W_{3} = {\frac{1}{2}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}}},{W_{4} = {\frac{1}{2}\begin{bmatrix}1 & j & {- 1} & {- j} \\{- j} & 1 & {- j} & 1 \\{- 1} & j & 1 & {- j} \\j & 1 & j & 1\end{bmatrix}}},{W_{5} = {\frac{1}{2}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}}},{W_{6} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & 1 & {- 1} \\{- 1} & 1 & 1 & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & {- 1} & 1 & 1\end{bmatrix}}},{W_{7} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & {- 1} & 1 \\{- 1} & 1 & {- 1} & 1 \\{- 1} & {- 1} & 1 & 1 \\1 & 1 & 1 & 1\end{bmatrix}}},{{W_{8} = {\frac{1}{2}\begin{bmatrix}1 & j & 1 & j \\{- j} & 1 & j & {- 1} \\1 & {- j} & 1 & {- j} \\{- j} & {- 1} & j & 1\end{bmatrix}}};}$an information receiver arranged to receive information associated witha matrix selected by a terminal from the stored codebook including atleast one W_(i); a matrix selector arranged to select a precoding matrixbased on information associated with the selected matrix; and a precoderarranged to perform precoding on a data stream to be transmitted usingthe selected precoding matrix.

In this instance, the information receiver may receive informationassociated with matrices corresponding to a plurality of terminals, inwhich the matrices are selected by the plurality of terminalsrespectively. The matrix selector may then select the precoding matrixbased on information associated with the matrices corresponding to theplurality of terminals.

Turning now to FIG. 5, a block diagram of a codebook generationapparatus for generating a codebook of precoding matrices for use in amulti-polarized MIMO system according to an example embodiment of thepresent invention is illustrated. Referring to FIG. 5, the codebookgeneration apparatus includes a single-polarized precoding matrixassignment unit 510, a zero matrix assignment unit 520, a precodingmatrix generation unit 530, a precoding matrix reconstruction unit 540,a rotated precoding matrix generation unit 550, and a phase adjustmentunit 560.

The single-polarized precoding matrix assignment unit 510 assigns asingle-polarized precoding matrix to each of diagonal blocks among aplurality of blocks within a block diagonal structure. The blocks areorganized according to a number of polarization directions oftransmitting antennas.

The zero matrix assignment unit 520 assigns a zero matrix to remainingblocks excluding the diagonal blocks within the block diagonalstructure.

The precoding matrix generation unit 530 generates a precoding matrixfor multi-polarized MIMO (i.e., a block diagonal multi-polarizedcodebook) by combining the single-polarized precoding matrices assignedto the diagonal blocks and the zero matrices assigned to the remainingblocks within the block diagonal structure.

The precoding matrix reconstruction unit 540 reconstructs the precodingmatrix by selecting, from the precoding matrix, at least one columnvector according to a transmission rank corresponding to a number ofdata streams to be transmitted.

The rotated precoding matrix generation unit 550 generates a rotatedprecoding matrix using the precoding matrix and a rotated matrixcorresponding to a rotated angle of the polarization direction when thepolarization direction of transmitting antennas is rotated.

The rotated precoding matrix generation unit 550 may generate areordered matrix by reordering column vectors that are included in theprecoding matrix, and generates the rotated precoding matrix by usingthe reordered matrix and the rotated matrix.

The phase adjustment unit 560 adjusts a phase of each of elementsincluded in the reordered matrix using a diagonal matrix.

Descriptions not made in relation to the apparatus of FIG. 5 will be thesame as the descriptions made with reference to FIGS. 1 through 4, andthus will be omitted.

Matrices included in a precoding matrix (block diagonal multi-polarizedcodebook) that is generated according to an aspect of the presentinvention will be stored in various types of communication apparatusesand used. For example, a communication apparatus may transmit andreceive data in a space division multiple access (SDMA) communicationsystem by using a matrix that is generated according to an aspect of thepresent invention. The communication apparatus may include various typesof devices for the SDMA communication system, such as a base station, arepeater, a terminal, and the like.

Specifically, a communication apparatus according to an aspect of thepresent invention may store a precoding matrix (block diagonalmulti-polarized codebook) that is generated by assigning asingle-polarized precoding matrix to diagonal blocks among a pluralityof blocks within a block diagonal structure that are divided ororganized according to the number of polarization directions oftransmitting antennas, and assigning a zero matrix to remaining blocksexcluding the diagonal blocks within the block diagonal structure.

According to an aspect of the present invention, the precoding matrix(block diagonal multi-polarized codebook) may be generated by combiningthe single-polarized precoding matrices assigned at diagonal blocks andthe zero matrices assigned at remaining blocks within the block diagonalstructure.

Also, a communication apparatus according to an aspect of the presentinvention may store a matrix that is reconstructed by selecting, fromthe precoding matrix, at least one column vector according to atransmission rank corresponding to a number of data streams to betransmitted.

Also, a communication apparatus according to an aspect of the presentinvention may store a rotated precoding matrix that is generated usingthe precoding matrix and a rotated matrix corresponding to a rotatedangle of the polarization direction when the polarization direction oftransmitting antennas is rotated.

Also, a communication apparatus according to an example embodiment ofthe present invention may generate a reordered matrix by reorderingcolumn vectors that are included in the precoding matrix, and store amatrix that is generated by using the reordered matrix and the rotatedmatrix.

When the communication apparatus is a base station (BS) used to supportmultiple user equipments (UEs) in a wireless network, such as 3GPP,Super 3G (3G Long Term Evolution “LTE”), 3GPP2 and upcoming 4G systems,the base station (BS) may transmit a transmission signal that beam formsa data stream using matrices included in the base station (BS).Specifically, the base station (BS) may include a codebook storage unitthat stores a codebook of matrices according to the present inventionand a beamformer that beam forms data streams using the stored matrices.

Conversely, when the communication apparatus is a terminal, the terminalmay generate feedback data using matrices selected from a codebookstored in the terminal. The feedback data is used when the base station(BS) performs beam-forming in which multiple data streams are emittedfrom transmitting antennas in accordance with matrices selected from acodebook stored in the terminal. Specifically, the terminal may includea codebook storage unit that stores a codebook of matrices according tothe present invention and a feedback data generation unit that generatesfeedback data corresponding to a wireless channel of the base stationusing the stored matrices.

According to aspects of the present invention, there is provided amethod and apparatus for generating a codebook for a multi-polarizedMIMO system that can generate a precoding matrix using asingle-polarized precoding matrix even when the polarization of antennasis multi-polarization, and thereby generate an excellent precodingmatrix that is easily generated. Such a codebook can be shared by atransmitter end and a receiver end.

Also, according to aspects of the present invention, there is provided amethod and apparatus for generating a codebook in a multi-polarized MIMOsystem that can reconstruct a precoding matrix according to atransmission rank and thereby can more effectively generate a codebook.

Also, according to aspects of the present invention, there is provided amethod and apparatus for generating a codebook in a multi-polarized MIMOsystem that can generate a rotated matrix when the polarizationdirection of transmitting antennas is rotated, and thereby can moreflexibly cope with a change in the polarization direction.

As described from the foregoing, a codebook with low complexity andexcellent performance and robustness can advantageously be obtained foruse in multi-polarized MIMO schemes. Such codebook design can also beused for single-polarized MIMO schemes without any significantperformance degradation.

Various components of the codebook generation apparatus, as shown inFIG. 5, such as, the single-polarized precoding matrix assignment unit510, the zero matrix assignment unit 520, the precoding matrixgenerating unit 530, the precoding matrix reconstruction unit 540, therotate precoding matrix generation unit 550 and the phase adjustmentunit 560 can be integrated into a single control unit, such as abaseband processor or controller located at a transmitter side, forexample, a base station, or alternatively, can be implemented insoftware or hardware, such as, for example, a field programmable gatearray (FPGA) and an application specific integrated circuit (ASIC). Assuch, it is intended that the processes described herein be broadlyinterpreted as being equivalently performed by software, hardware, or acombination thereof. As previously discussed, software modules can bewritten, via a variety of software languages, including C, C++, Java,Visual Basic, and many others. These software modules may include dataand instructions which can also be stored on one or moremachine-readable storage media, such as dynamic or static random accessmemories (DRAMs or SRAMs), erasable and programmable read-only memories(EPROMs), electrically erasable and programmable read-only memories(EEPROMs) and flash memories; magnetic disks such as fixed, floppy andremovable disks; other magnetic media including tape; and optical mediasuch as compact discs (CDs) or digital video discs (DVDs). Instructionsof the software routines or modules may also be loaded or transportedinto the wireless cards or any computing devices on the wireless networkin one of many different ways. For example, code segments includinginstructions stored on floppy discs, CD or DVD media, a hard disk, ortransported through a network interface card, modem, or other interfacedevice may be loaded into the system and executed as correspondingsoftware routines or modules. In the loading or transport process, datasignals that are embodied as carrier waves (transmitted over telephonelines, network lines, wireless links, cables, and the like) maycommunicate the code segments, including instructions, to the networknode or element. Such carrier waves may be in the form of electrical,optical, acoustical, electromagnetic, or other types of signals.

In addition, the codebook generating method as shown in FIG. 2 may berecorded in computer-readable media including program instructions toimplement various operations embodied by a computer. The media may alsoinclude, alone or in combination with the program instructions, datafiles, data structures, and the like. Examples of computer-readablemedia include magnetic media such as hard disks, floppy disks, andmagnetic tape; optical media such as CD ROM disks and DVD;magneto-optical media such as optical disks; and hardware devices thatare specially configured to store and perform program instructions, suchas read-only memory (ROM), random access memory (RAM), flash memory, andthe like. The media may also be a transmission medium such as optical ormetallic lines, wave guides, and the like, including a carrier wavetransmitting signals specifying the program instructions, datastructures, and the like. Examples of program instructions include bothmachine code, such as produced by a compiler, and files containinghigher level code that may be executed by the computer using aninterpreter. The described hardware devices may be configured to act asone or more software modules in order to perform the operations of theabove-described embodiments of the present invention.

While there have been illustrated and described what are considered tobe example embodiments of the present invention, it will be understoodby those skilled in the art and as technology develops that variouschanges and modifications, may be made, and equivalents may besubstituted for elements thereof without departing from the true scopeof the present invention. Many modifications, permutations, additionsand sub-combinations may be made to adapt the teachings of the presentinvention to a particular situation without departing from the scopethereof. For example, the antenna arrangement, shown in FIGS. 1A-1C,typically includes a transmitter side provided with transmittingantennas X₁ . . . X_(M) and a receiver side provided with N receiverantennas Y₁ . . . Y_(N) to communicate, via a wireless channel (channelmatrix H). For mobile communication systems, a base station (BS), knownas “Node-B” as specified in accordance with 3GPP, 3GPP2 and 4Gspecifications, is used at the transmitter end to transmit data, viawireless channels. User equipments (UEs), typically mobile stations(MS), are used at the receiver end to receive data, via the wirelesschannels. Such user equipments (UE) can be, for example, mobile phones(handsets), personal digital assistants (PDAs), or other devices such aswireless cards in laptop computers or computers with internet wirelessconnectivity, WiFi and WiMAX gadgets etc. The wireless network can bethat of any of the wireless communication technologies, including, butnot limited to GSM (Global System for Mobile Communications), CDMA (CodeDivision Multiple Access), WLL (Wireless Local Loop), WAN (Wide AreaNetwork), WiFi, and WiMAX (Worldwide Interoperability for MicrowaveAccess based on IEEE 802.16 standards), and is applicable with manyexisting and emerging wireless standards such as IEEE 802.11 (forwireless local area networks), IEEE 802.16 (for wireless metropolitanarea networks) and IEEE 802.02 (for mobile broadband wireless access).The base station (BS) can also be an IEEE 802.11 access point (AP) andthe UE can also be any client station. Alternatively, the base stationcan also be implemented with a GERAN (GSM/EDGE radio access technology)in a UTRAN (UMTS Terrestrial Radio Access Network) using a wideband codedivision multiple access (WCDMA) technology. However, the invention isnot limited to those radio access technologies, but it can also beapplied to the following radio access technologies: GSM (Global Systemfor Mobile Communications), GPRS (General Packet Radio Service), E-GPRS(EDGE GPRS), CDMA2000 (CDMA, Code Division Multiple Access), US-TDMA (USTime Division Multiple Access), and IS-95. Accordingly, it is intended,therefore, that the present invention not be limited to the variousexample embodiments disclosed, but that the present invention includesall embodiments falling within the scope of the appended claims.

What is claimed is:
 1. A terminal comprising: a codebook storage unitconfigured to store information associated with a codebook includingmatrices: ${\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}},{and}$ ${\frac{1}{2}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}};$ a selector configured to select a target matrix fromthe stored information associated with the codebook; and an informationfeedback unit configured to feed back information associated with thetarget matrix to a base station.
 2. The terminal as claimed in claim 1,wherein the selector selects the target matrix from the informationassociated with the codebook based on the state of a wireless channelformed between the terminal and the base station.
 3. The terminal asclaimed in claim 1, wherein the selector selects the target matrix fromthe codebook based on an achievable data transmission rate.
 4. Theterminal as claimed in claim 1, wherein the codebook further includes amatrix ${\frac{1}{2}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}}.$
 5. The terminal as claimed in claim 1, wherein theselector selects the target matrix from the codebook and selects atleast one column vector from column vectors included in the selectedtarget matrix, and the information feedback unit feeds back to the basestation the information associated with the selected target matrix andinformation associated with the selected at least one column vector. 6.The terminal as claimed in claim 5, wherein the information feedbackunit feeds back to the base station index information of the selectedtarget matrix and index information of the selected at least one columnvector.
 7. A method of operating a terminal, the method comprising:receiving a pilot signal transmitted from a base station; storinginformation associated with a codebook including matrices:${\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}},{and}$ ${\frac{1}{2}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}};$ selecting a target matrix from the codebook in responseto receiving the pilot signal; and feeding back information associatedwith the target matrix to the base station.
 8. A base stationcomprising: a codebook storage unit to store information associated witha codebook including matrices: ${\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}},{and}$ ${\frac{1}{2}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}};$ an information receiver to receive informationassociated with a matrix selected by a terminal from the codebook; amatrix selector to select a precoding matrix based on the informationassociated with the selected matrix; and a precoder to perform precodingon a data stream to be transmitted using the selected precoding matrix.9. The base station as claimed in claim 8, wherein: the informationreceiver receives information associated with matrices selected by aplurality of terminals, respectively, and the matrix selector selectsthe precoding matrix based on the information associated with thematrices selected by the plurality of terminals.
 10. The base station asclaimed in claim 8, wherein the codebook further includes a matrix${\frac{1}{2}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}}.$
 11. A method of operating a base station, the methodcomprising: storing information associated with a codebook includingmatrices: ${\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}},{and}$ ${\frac{1}{2}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}};$ selecting a precoding matrix from the codebook; andperforming precoding on a data stream to be transmitted using theselected precoding matrix.
 12. The method of claim 7, wherein thecodebook further includes a matrix ${\frac{1}{2}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}}.$
 13. The method of claim 7, wherein the target matrix isselected from the codebook based on the state of a wireless channelformed between the terminal and the base station.
 14. The method ofclaim 7, further comprising: selecting at least one column vector fromcolumn vectors included in the selected target matrix, and feeding backto the base station information associated with the selected at leastone column vector.
 15. The method of claim 14, wherein: the informationassociated with the selected target matrix is index information, and theinformation associated with the selected at least one column vector isindex information.
 16. The method of claim 11, wherein the codebookfurther includes a matrix ${\frac{1}{2}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}}.$
 17. The method of claim 11, further comprising:receiving information associated with selected matrices from thecodebook, each of the selected matrices selected by a different one of aplurality of terminals, wherein the precoding matrix is selected basedon information associated with the matrices.